Before giving our main results, let us consider the following lemma
found in [1]} that gives a necessary and sufficient
condition for a graph to be super edge-magic.
 
A graph \(G\)  with \(v\)  vertices and \(e\)  edges is super edge-magic
if and only if there exists a bijective function \(\lambda :V(G)\rightarrow \lbrace 1, 2, \cdots , v\rbrace \)  such that the set \(S = \lbrace \lambda (x) +\lambda (y) | xy \in E(G)\rbrace \)  consists of \(e\)  consecutive integers. In such
a case, \(\lambda \)  extends to a super edge-magic labeling of \(G\)  with
magic constant \(c = v + e + s\) , where \(s = min(S).\)
